Question

5. Let a, b, and c be positive integers. Use congruence mod 4 to prove the given statement. If $3^a + 4^b = 5^c$, then a must be even.

          5. Let a, b, and c be positive integers.
Use congruence mod 4 to prove the given statement.
If $3^a + 4^b = 5^c$, then a must be even.

Added by Charles K.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Gregory Higby

Step 1

First, let's write down the given statement: a^2 + b^2 + c^2 ≡ 0 (mod 4) To prove this statement using congruence modulo 4, we need to show that the left-hand side (a^2 + b^2 + c^2) is congruent to the right-hand side (0) modulo 4. Show more…

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Let a, b, and c be positive integers. Use congruence modulo 4 to prove the given statement.

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5. Let a, b, and c be positive integers. Use congruence mod 4 to prove the given statement. If $3^a + 4^b = 5^c$, then a must be even.

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